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Answer 1

Question

The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm then find the remaining sides.

Solution

Length of the hypotenuse of the triangle = 25 cm

Let the lengths of other base and height be x, y respectively.

Perimeter of the triangle = 60 cm

⇒ Sum of length of all sides = 60 cm

⇒ x + y + 25 = 60

⇒ x + y = 60 - 25

⇒ x + y = 35

⇒ y = 35 - x

By pythagoras theorem

⇒ (Base)² + (Height)² = (Hypotenuse)²

⇒ x² + y² = 25²

⇒ x² + (35 - x)² = 625

⇒ x² + 35² - 2(35)(x) + x² = 625

⇒ 2x² + 1225 - 70x = 625

⇒ 2x² - 70x + 1225 - 625 = 0

⇒ 2x² - 70x + 600 = 0

⇒ 2(x² - 35x + 300) = 0

⇒ x² - 35x + 300 = 0

⇒ x² - 15x - 20x + 300 = 0

⇒ x(x - 15) - 20(x - 15) = 0

⇒ (x - 20)(x - 15) = 0

⇒ x - 20 = 0 or x - 15 = 0

⇒ x = 20 or x = 15 cm

i.e Base = x = 20 or 15 cm

Therefore, the remaining 2 sides measure 20 cm and 15 cm